Mixed Sensitivity Problem Research Articles

Fractional Order Weighted Mixed Sensitivity-Based Robust Controller Design and Application for a Nonlinear System

This paper focuses on fractional-order modeling and the design of a robust speed controller for a nonlinear system. An induction motor (IM), widely used in Electrical Vehicles (EVs), is preferred in this study as a well-known nonlinear system. The major challenge in designing a robust speed controller for IM is the insufficiency of the machine model due to inherent machine dynamics. Fractional calculus is employed to model the IM using the small-signal method, accounting for model uncertainties. In this context, experimental data is approximated using a fractional-order small-signal transfer function. Consequently, a mixed sensitivity problem is formulated with fractional-order weighting functions. The primary advantage of these weighting functions is their greater flexibility in solving the mixed sensitivity problem by involving more coefficients. Hereby, three robust speed controllers are designed using the PID toolkit of the Matlab program and solving the H∞ mixed sensitivity problem, respectively. The novelty and contribution of the proposed method lie in maintaining the closed-loop response within a secure margin determined by fractional weighting functions while addressing the controller design. After evaluating the robust speed controllers with Bode diagrams, it is proven that all the designed controllers meet the desired nominal performance and robustness criteria. Subsequently, real-time implementations of the designed controllers are performed using the dsPIC microcontroller unit. Experimental results confirm that the designed H∞-based fractional-order proportional-integral-derivative (FOPID) controller performs well in terms of tracking dynamics, exhibits robustness against load disturbances, and effectively suppresses sensor noise compared to the robust PID and fixed-structured H∞ controller.

외란과 모델 불확실성이 존재하는 가변속 냉동시스템의 강인제어를 위한 H-infinity 제어기 설계

This paper describes the design of H-infinity controller for robust control of a variable speed refrigeration system. The suggested controller can ensure robustness against disturbance and model uncertainty by minimizing H-infinity norm of the transfer function from exogenous input to performance output and applying the small gain theorem. In particular, the controller was designed to simultaneously reduce the effects of disturbance and model uncertainty by formalizing these problems as a mixed sensitivity problem. In addition, an integrator was included to the controller to prevent the occurrence of steady state error. The validity of the proposed controller was demonstrated by computer simulations and real experiments. Moreover, the effectiveness of the proposed controller was confirmed by comparing its performance to the PI controller, which was tested under the same experimental conditions as the H-infinity controller.

A robust LQR-FOPIλDµ controller design for output voltage regulation of stand-alone self-excited induction generator

This paper presents several optimal controllers compared with a robust control method for the terminal voltage regulation of a stand-alone self-excited induction generator (SEIG) with fixed capacitor and thyristor controlled reactor (FC-TCR). The major challenge of designing process of the controllers is the nonexistence of perfect model of SEIG. Therefore, small-signal based models for the output voltage and frequency are carried out using real input-output data. Accordingly, Linear Quadratic Regulator (LQR), Linear Quadratic Integral (LQI) and Linear Quadratic Fractional Order Integral (LQFOIλ) controllers are designed to regulate output voltage. Moreover, novelty and main contribution of the paper is to design a hybrid controller which combines LQR and Fractional Order Proportional Integral Derivative (LQR-FOPIλDµ) controller to ensure the best tracking dynamics, robustness against disturbances and sensor noise suppression. The proposed hybrid LQR-FOPIλDµ controller is obtained by solving H∞ weighted mixed sensitivity problem. Optimization process of the controller parameters is implemented by using particle swarm optimization (PSO) algorithm. Matlab/Simulink program is used to compare the effectiveness of the proposed controllers. Furthermore, the experimental results show that robust LQR-FOPIλDµ controller has the best tracking dynamics among them with less overshoot, settling time as well as the robust structure against external disturbances and sensor noises.

WITHDRAWN: Design of Robust Pole Configuration Controller Based on Embedded Network Distributed Single Input System

Abstract Robust control methods today are primarily solutions and the optimization process is presented as a set of optimization problems depends on the mathematical properties of the objective function. The proposed method, solving a polynomial equation based on the fixed characteristic polynomial is selected, including introducing a parameter solution having a known parameter structure of the controller.The embedded controller model should be modified to include an input / output interface with an external device. The method also includes a common reference function, which allows the possibility of different unrelated may consist of a standard, multi-objective optimization strict standard, mixed sensitivity problem applications, and other closed-loop constraints. Optimized design of the controller, clustering K- means the algorithm is executed.The following control performance parameters at different time and frequency domain studies, and is uncertain process parameters deviations thereof. Controller tuning rules are used for the process using a test bench, and it also the computational complexity analysis and process algorithms dynamics and sampled non- dominant pole type different types of distribution of data point's stable solution that provides an implementation of the hypothesis test for robustness. In the best case, these control law with single-precision (32-bit) arithmetic is implemented in the embedded processor.

Control law for line of sight stabilization in two-axis gimbal system

A two-axis gimbaled stabilization system in air vehicles must stabilize the line of sight of the payload toward a target against the external motion induced by air vehicle maneuvering and aerodynamic forces. The target tracking and pointing performances of the air vehicles are largely affected by air vehicle motion decoupling capability. In this work, the controller design is carried out for a two-axis gimbal system. The plant model is generated using experimental frequency response data and mathematical formulation of the system. The mixed sensitivity problem is posed and weighting functions are selected so that they not only fulfill all the design goals but also accommodate the modeling uncertainties. The stabilization loop is designed and implemented in digital signal processor-based hardware for only one axis (in azimuth).

H ∞ robust control with improved harmonics suppression for inverter‐based distributed generation systems

Voltage source inverter is a key element in an inverter-based distributed generation (DG) system for the integration of renewable energy resources with an existing power grid. Interconnection standards for the requirements of inverter output current quality are one of the foremost demands imposed by distribution system operators. The operation of a stabilised DG system with LCL -filter meeting current quality requirements is challenging due to variation in system parameters and non-ideal grid voltages. In this context, this study proposes a robust controller design and modified control structure to improve current quality in the presence of distorted grid voltages. The controller is designed based on general mixed sensitivity problem formulation to achieve robustness against system parameters variation and ensure high-quality injected current under normal grid voltage. The control performance of the designed robust controller with a feed-forward loop is investigated under distorted grid voltage. Furthermore, an inverter current compensation is proposed, employed by an additional inverter current feedback loop through the high-pass compensator. The current quality investigation with variation in different parameters and low power operation shows enhanced control performance of the proposed solution under distorted as well as normal grid voltages. The main features of the proposed scheme are the simplicity in design, easy implementation, and better harmonics rejection capability without limiting the control loop stability. The simulation and experimental results validate the effectiveness of the proposed method .

Observer‐based synthesis of linear parameter‐varying mixed sensitivity controllers

SummaryThis article presents a computationally efficient way of synthesizing linear parameter‐varying (LPV) controllers. It reviews the possibility of a separate observer and state feedback synthesis with guaranteed performance and shows that a standard mixed sensitivity problem can be solved in this way. The resultant output feedback controller consists of an LPV observer, augmented with dynamic filters to incorporate integral control and roll‐off properties, and an LPV state feedback gain. It is thus highly structured, which is beneficial for implementation. Moreover, it does not depend on scheduling parameter rates regardless of whether parameter‐dependent Lyapunov matrices are used during synthesis. A representative control design for active flutter suppression on an aeroelastic unmanned aircraft demonstrates the benefits of the proposed method in comparison with state‐of‐the‐art LPV output feedback synthesis.

H∞ active control of frequency-varying disturbances in a main engine on the floating raft vibration isolation system

Reducing the vibration of marine power machinery can improve warships' capabilities of concealment and reconnaissance. Being one of the most effective means to reduce mechanical vibrations, the active vibration control technology can overcome the poor effect in low frequency of traditional passive vibration isolation. As the vibrations arising from operation of marine power machinery are actually the frequency-varying disturbances, the H∞ control method is adopted to suppress frequency-varying disturbances. The H∞ control method can solve the stability problems caused by the uncertainty of the model and reshape the frequency response function of the closed loop system. Two-input two-output continuous transfer function models were identified by using the system identification method and are validated in frequency domain of which all values of best fit exceeds 89%. The method of selecting the weighting functions on the mixed sensitivity problem is studied. Besides, the H∞ controller is designed for a multiple input multiple output (MIMO) system to suppress the single-frequency-varying disturbance. The numerical simulation results show that the magnitudes of the error signals are reduced by more than 50%, and the amplitudes of the dominant frequencies are attenuated by more than 10 dB. Finally, the single excitation source dual-channel control experiments are conducted on the floating raft isolation system. The experiment results reveal that the root mean square values of the error signals under control have fallen by more 74% than that without control, and the amplitudes of the error signals in the dominant frequencies are attenuated above 13 dB. The experiment results and the numerical simulation results are basically in line, indicating a good vibration isolation effect.

Robustified fractional-order controller based on adjustable fractional weights for a doubly fed induction generator

In this paper, a robustification method of the primary fractional controller is proposed. This novel method uses the adjustable fractional weights on the H∞ mixed-sensitivity problem. It can achieve an enhancement in both nominal performance and robust stability margins for the uncertain plants while respecting the frequency-domain constraints, such as the tracking of the set-point references, load disturbance attenuation and measurement noise suppression. The proposed robustification holds two steps; in the first step, a primary fractional controller is designed from solving the H∞ mixed-sensitivity problem that uses fixed-integer weights. In the second step, the robustified fractional controller with adjustable fractional weights is designed in order to guarantee a good compromise between the nominal performance and the robust stability not only for the nominal plant, but also for all set of the neighbouring plants. The proposed robustified fractional controller is used to control the doubly fed induction generator. Its dynamic is modelled by the unstructured output-multiplicative uncertain plant. Simulation results given by both primary and robustified fractional controllers are compared in time and frequency domains with those given by the conventional integer H∞ controller in order to validate the effectiveness of the proposed method.

Identification-Based Robust Motion Control of an AUV: Optimized by Particle Swarm Optimization Algorithm

In this paper, the problem of identification-based robust motion control of an Autonomous Underwater Vehicle (AUV) is investigated. The unknown system parameters are estimated by using an adaptive parameter identifier, whose gains are optimized by Particle Swarm Optimization (PSO) algorithm. Removing the trial and error procedure and ensuring the convergence property together with fast response, are the benefits of such identification scheme. On the other hand, the system uncertainties, hydrodynamic parameter variations and external disturbances which affect the identified dynamical model, are also taken into account. The cross-coupling effects between subsystems are also considered as model uncertainties. Such uncertain model is then adopted in control synthesis procedure, in the steering and diving modes. In order to achieve the robust stability and performance, two robust control strategies are presented here to solve the motion control problem. First, an Hź$H_{\infty }$ mixed sensitivity problem is formulated in which the weighting functions are selected based on an optimization criterion, by using PSO algorithm. Controller order reduction is also applied to the resulting diving and steering controllers, using the Hankel norm approximation. Then, an Adaptive Sliding Mode Control (ASMC), whose sliding surface coefficients are optimized by PSO algorithm, is developed for the identified AUV model. Possessing the robustness properties with respect to system perturbations, the developed Sliding Mode Control (SMC) removes the complexity of uncertain model representation and the limitations on choosing the weighting functions in the Hź$H_{\infty }$ control problem. The upper bounds of perturbations are not required to be known in the proposed control schemes. The simulation results are also presented to demonstrate the performance of the proposed identification-based control methods.

Tilt-rotor multivariable attitude control with rotor state feedback

In this paper, a multi-objective optimization-based methodology for rotorcraft attitude control law design is applied to a tilt-rotor case; the framework allows to enforce requirements of stability, performance, control action moderation, and safety. The structured H∞ approach is taken into account, and the optimization problem is stated as a mixed-sensitivity problem. Rotor state feedback is used to limit flap motion, and is introduced as an additional loop to a classical attitude control law.

Controllability analysis and robust control of a one-stage refrigeration system

This paper describes the controllability analysis and the design of a multivariable robust controller for a one-stage refrigeration cycle, which is the most used system for cooling issues and whose energy management and control are key factors. The controlled variables are the superheating degree of refrigerant at the evaporator outlet and the outlet temperature of evaporator secondary flux, whereas the control variables are the electronic expansion valve opening and the compressor speed. The system is considered therefore as a MIMO one. Up to eight different operating points are identified in order to design the multivariable H∞ controller based on the S/KS/T Mixed Sensitivity Problem. Simulation results comparing this controller to a decentralised PID and to a multivariable predictive one are shown, proving a better performance of the robust controller as well as accomplishment with the controllability analysis conclusions.

Multivariable analysis and H∞ control of a one-stage refrigeration cycle

In this paper the robust control of a one-stage refrigeration cycle is addressed. This is a MIMO process, where the expansion valve opening and the compressor speed are used as manipulated variables, whereas the control of both the outlet temperature of evaporator secondary flux and the superheating degree of refrigerant at evaporator outlet is intended. After the identification of the system at several operating points, a controllability analysis is carried out and a multivariable robust H∞ controller is designed, using the S/KS/T Mixed Sensitivity Problem approach. Simulation results concerning reference tracking, coupling measurement and disturbance rejection are included, comparing the H∞ controller to a decentralised PID one. Better closed-loop performance of the robust controller and reduced coupling between controlled variables are observed, as well as agreement with the controllability analysis conclusions regarding rise time bounds. A versatile experimental plant designed and set up by the authors is also described. As future work it is expected that identification and comparison between simulation and actual results can be achieved.

Multiloop robust H∞ control design based on the dynamic PLS approach to chemical processes

In this paper, a multiloop robust control strategy is proposed based on H∞ control and a partial least squares (PLS) model (H∞_PLS) for multivariable chemical processes. It is developed especially for multivariable systems in ill-conditioned plants and non-square systems. The advantage of PLS is to extract the strongest relationship between the input and the output variables in the reduced space of the latent variable model rather than in the original space of the highly dimensional variables. Without conventional decouplers, the dynamic PLS framework automatically decomposes the MIMO process into multiple single-loop systems in the PLS subspace so that the controller design can be simplified. Since plant/model mismatch is almost inevitable in practical applications, to enhance the robustness of this control system, the controllers based on the H∞ mixed sensitivity problem are designed in the PLS latent subspace. The feasibility and the effectiveness of the proposed approach are illustrated by the simulation results of a distillation column and a mixing tank process. Comparisons between H∞_PLS control and conventional individual control (either H∞ control or PLS control only) are also made.

Control Design of Mixed Sensitivity Problem for Educational Model of Helicopter

The paper deals with the design of H-∞ robust controller, particularly with mixed sensitivity problem for elevation control. It briefly introduces basic mathematical background concerning robust control approach, which is then applied for typical example of MIMO system, that is a helicopter model. The obtained results are verified on real educational physical model CE 150 by Humusoft, ltd.

On the structure of generalized plant convexifying static [formula omitted] control problems

This paper shows that, under specific structures of generalized plants, the set of static controllers satisfying internal stability and a certain level of H∞ performance becomes convex. More precisely, we characterize such static H∞ controllers by an LMI with controller variables being kept directly as decision variables. The structural conditions on the generalized plant are not too strict, and we show that generalized plants corresponding to a sort of mixed sensitivity problems indeed satisfy these conditions. For the generalized plants of interest, we further prove that full-order dynamical H∞ controllers can be characterized by an LMI with a simple change of variables. In stark contrast to the known LMI-based H∞ controller synthesis, the change of variables is free from the coefficient matrices of the generalized plant and this property is promising when dealing with a variety of robust control problems. Related issues such as robust controller synthesis against real parametric uncertainties are also discussed.

21410 鉄道車両のアクティブサスペンションによる振動制御

A high speed railway vehicle is greatly affected by track irregularity. Vertical vibration of a high speed railway vehicle makes worse the ride comfort of passengers. This paper aims at reducing such vibration, especially the 1st mode bending vibration of carbody with the active suspension system. This system used the proposed method of designing a vibration control system. The controller was designed by applying the mixed sensitivity problem of H-infinity control theory. The numerical simulation results show that the ride comfort of passengers is improved by the active suspension.

Position and Current Control of an Interior Permanent-Magnet Synchronous Motor by Using Loop-Shaping Methodology: Blending of H∞ Mixed-Sensitivity Problem and T–S Fuzzy Model Scheme

This paper presents a robust mixed-sensitivity H∞ controller design via loop-shaping methodology for a class of multiple-input multiple-output (MIMO) uncertain nonlinear systems. In order to design this controller, the nonlinear plant is first modeled as several linear subsystems by Takagi and Sugeno's (T–S) fuzzy approach. Both loop-shaping methodology and mixed-sensitivity problem are then introduced to formulate frequency-domain specifications. Afterward for each linear subsystem, a regional pole-placement output-feedback H∞ controller is employed by using linear matrix inequality (LMI) approach. The parallel distributed compensation (PDC) is then used to design the controller for the overall system. Several experimental results show that the proposed method can effectively meet the performance requirements like robustness, good load disturbance rejection, and both tracking and fast transient responses even in the presence of parameter variations and load disturbance for the three-phase interior permanent-magnet synchronous motor (IPMSM). Finally, the superiority of the proposed control scheme is approved in comparison with the input–output linearization (I/O linearization) and the H2/H∞ controller methods.

Mixed Sensitivity H-∞ Control for Helicopter Model

The paper deals with the design of H-∞ robust controller, particularly with mixed sensitivity problem for elevation control. It briefly introduces basic mathematical background concerning robust control approach, which is then applied for typical example of MIMO system, that is a helicopter model. The obtained results are verified on real educational physical model CE 150 by Humusoft, ltd.

H∞ Based Control for Load Mitigation in Wind Turbines

This article demonstrates a strategy to design multivariable and multi-objective controllers based on the H∞ norm reduction applied to a wind turbine. The wind turbine model has been developed in the GH Bladed software and it is based on a 5 MW wind turbine defined in the Upwind European project. The designed control strategy works in the above rated power production zone and performs generator speed control and load reduction on the drive train and tower. In order to do this, two robust H∞ MISO (Multi-Input Single-Output) controllers have been developed. These controllers generate collective pitch angle and generator torque set-point values to achieve the imposed control objectives. Linear models obtained in GH Bladed 4.0 are used, but the control design methodology can be used with linear models obtained from any other modelling package. Controllers are designed by setting out a mixed sensitivity problem, where some notch filters are also included in the controller dynamics. The obtained H∞ controllers have been validated in GH Bladed and an exhaustive analysis has been carried out to calculate fatigue load reduction on wind turbine components, as well as to analyze load mitigation in some extreme cases. The analysis compares the proposed control strategy based on H∞ controllers to a baseline control strategy designed using the classical control methods implemented on the present wind turbines.